Scale/Dimension change when I add a curve modifier
Solution Found!! :D

Modifying the dimensions of the objects in EDIT mode solves the issue. It seems that my previous method of modifying dimensions in OBJECT mode does not actually modify the dimensions but applies a transform to the objects. And when the plane gets associated to the curve via the modifier, it seems that the transform of the curve gets also applied to the plane, which results in the weird change in dimensions I was observing.

Anyway, problem solved... Thanks to all those who tried to help!